While we are inspired by known GPT models [1]}, [2]}, [3]}, [4]}, [5]}, we take a slightly different and simplified approach here.
The idea is that agents only have direct access to classical random variables (like input settings and outputs of a physical measurement). Since they correspond to accessible information, we denote probability distributions over these random variables by states.
Transformations \(f\)  are naturally modelled by conditional probability distributions \(P^f_{Z|X}\)  that take input to output states, such that
\(f( P_X ) = P^{\prime }_{Z}\) , with
\(P^{\prime }_Z(Z) &= \sum _{x\in X} P^f_{Z|X}(z|x)\ P_X(x).\) 
